let ( h(x)=\frac{1}{x^{6}} ). ( h^{prime}(1)= )
let ( h(x)=\frac{1}{x^{6}} ). ( h^{prime}(1)= )
Answer
Explanation:
Step1: Rewrite the function
Rewrite ( h(x)=\frac{1}{x^{6}} ) as ( h(x)=x^{-6} ).
Step2: Apply the power rule
The power rule is ( (x^{n})^\prime = nx^{n - 1} ). For ( h(x)=x^{-6} ), ( h^\prime(x)=-6x^{-6 - 1}=-6x^{-7}=-\frac{6}{x^{7}} ).
Step3: Substitute ( x = 1 )
Substitute ( x = 1 ) into ( h^\prime(x) ). ( h^\prime(1)=-\frac{6}{1^{7}}=-6 ).
Answer:
(-6)